Page 205 - Modern physical chemistry

B.11 Equilibria Among Phases Revisited 197

and
J1.Avl BV2 = v1J1.1 + v2J1.2· [8.102J

The chemical potential per equivalent is

[8.103J

Thus, equation (8.100) tells us that the chemical potential of each strong electrolyte
is the same in each phase at equilibrium; we have

(1) _ (2) [8.104J
J1.AVl B V2 - J1.AVl B V2 •
One may also define the activity of the electrolyte a by the equation

J1.AVl BV2 = J1.1 Vl BV2 + RTlna. [8.105J

Then (8.104) can be rewritten as

/(1) +RTlna(1)=J1.*) +RTlna(2). [8.106J
AVl BV2 AVl BV2
When the standard state is the same in both phases, the standard chemical potentials
are the same and we have
[8.107J
The activity of the electrolyte in one phase equals its activity in a phase in equilibrium
with the first phase.
But for equilibrium between a pure crystal and a solution at 1 bar, we take the activ-
ity of the crystal to be 1 unit. Then for the solution, we have

[8.108J
whence

[8. 1 09J

or
[8.110J
where K is the equilibrium constant.
For the cation and for the anion in a given solution, one has
o
J1.1 = J1.1 +RTlna1, [8.111 J
o [8.112J
J1.2 = J1.2 + RTlna2'
But substituting (8.105), (8.111), and (8.112) into (8.102) yields
o 0 0
J1. A B +RTlna=v1J1.1 +v1RTlna1+v2J1.2 +v2RTlna2' [8.113J
Vl V2
Then subtracting the equation
000
J1. A B = v1J1.1 + v2J1.2 [8.114J
Vl V2